Simulation method for dynamic characteristics of wheeltrack type belt conveyor

Abstract

The invention relates to the technical field of belt conveyor dynamic characteristic research, in particular to a wheel track type belt conveyor dynamic characteristic simulation method, which comprises the following steps of: establishing dynamic models of a conveying belt, a vehicle supporting device, a tensioning device and a driving device, setting dynamic parameters and boundary conditions and initial conditions of the dynamic models, and calculating dynamic characteristics of the conveying belt, the vehicle supporting device, the tensioning device and the driving device. And compiling a calculation program by using numerical calculation software, and simulating the vibration condition of the conveying belt at a bearing section and the vibration condition of the conveying belt passing through a track gap when the conveying belt runs at a constant speed. According to the method, the MATLAB is used for numerical calculation simulation analysis, and the dynamic response condition of vibration in the advancing process of the conveying belt can be accurately subjected to simulation analysis; and the MATLAB numerical simulation result is verified in combination with a three-dimensional simulation mode, so that the accuracy of the simulation result is ensured.

Description

Technical Field

[0001] The invention relates to the technical field of research on dynamic characteristics of belt conveyors, in particular to a method for simulating dynamic characteristics of wheel-rail belt conveyors. Background Art

[0002] Belt conveyors are widely used in the transportation link of the coal industry. For long-distance off-road belt conveyors, wheel-rail belt conveyors can effectively reduce the running resistance. However, the wheel-rail belt conveyor introduces a wheel-rail running device, which causes more obvious vibration and impact during operation. In particular, the longitudinal vibration along the direction of movement has a greater impact on the smooth operation of the conveyor, and in severe cases can cause major safety accidents. When the belt conveyor is running at a low speed, the change in its dynamic characteristics is relatively small, but now the belt conveyor has developed in the direction of high speed, long distance, and large capacity, especially the complex and changeable off-road belt conveyor. Due to the viscoelastic characteristics of the conveyor belt, it presents complex dynamic characteristics, but the existing schemes still lack methods for accurately studying its dynamic characteristics. Summary of the invention

[0003] The present invention aims to solve the above problems and provides a method for simulating the dynamic characteristics of a wheel-rail belt conveyor. The technical solution adopted is as follows: A method for simulating dynamic characteristics of a wheel-rail belt conveyor, wherein the wheel-rail belt conveyor comprises a trolley track, a rotating wheel, a trolley device, a driving device, a conveyor belt and a tensioning device, wherein the rotating wheel and the trolley track form a closed loop structure, and the rotating wheel is arranged at both ends of the trolley track, the number of the trolley devices is multiple, and the trolley devices are driven by the driving device and move on the trolley track and the rotating wheel, the trolley device comprises a vehicle body and front wheels and rear wheels which are respectively rotatably connected at the front and rear ends of the vehicle body; the upper trolley track between the two rotating wheels is defined as a load-bearing section, and the lower trolley track is defined as a return section, and the conveyor belt is arranged on the trolley device at the load-bearing section and the return section and moves synchronously with the trolley device; The downward direction perpendicular to the conveyor belt surface of the load-bearing section is defined as the vertical direction, and the moving direction of the vehicle body along the trailer track is defined as the longitudinal direction; The method for simulating the dynamic characteristics of a wheel-rail belt conveyor includes the following steps: S1. Assume that the trailer vibrates only in the vertical direction, and the force exerted by the driving device on the trailer is always in the longitudinal direction; assume that each trailer device is an independent unit, and the conveyor belt corresponding to the trailer device is defined as an independent unit, and the mass of each independent unit is concentrated at the center of mass; simplify the conveyor belt of each independent unit into a spring and a damper, where the spring is an ideal linear spring and the damper is an ideal viscous damper; S2. Establish the independent unit dynamic model of the conveyor belt based on the Kelvin-Voigt model; S3. Establish a mechanical equilibrium equation for the trailer device, establish a vehicle body vertical displacement equation and a vehicle body pitch displacement equation according to the Hamilton principle, and then obtain a linear second-order differential equation of an independent unit of the trailer device; S4. Establish a mechanical equilibrium equation for the tensioning device, combine the independent units of the two conveyor belts adjacent to the tensioning device, and establish a dynamic model of the tensioning device according to the Euler-Lagrange equation; S5. Establish a dynamic model of the driving device; S6. Combine the mathematical models of S2 and S5 to establish the overall dynamic model of the conveyor belt; S7. Determine the dynamic parameters of the dynamic model in step S6, wherein the dynamic parameters include mass, stiffness, damping and external force; S8. Setting the initial conditions and boundary conditions of the dynamic model in step S6; S9. Use numerical calculation software to compile the calculation program to simulate the vibration of the conveyor belt at the load-bearing section and the vibration of the conveyor belt passing through the track gap when the conveyor belt runs at a constant speed.

[0004] Based on the above scheme, step S2 is: The constitutive model of the spacing between the core material and the steel wire rope is established along the width direction of the core, and then the equilibrium equation of the independent unit of the conveyor belt is established. (2-1) in is the stress of the conveyor belt as a whole, is the stress on the wire rope, is the stress on the upper and lower covering layers, is the overall strain of the conveyor belt, is the strain of the wire rope, is the stress on the upper and lower covering layers, It is the volume coefficient of a single steel wire rope in the entire conveyor belt; is the elastic modulus of the wire rope, is the elastic modulus of the upper and lower covering layers, is the Riemann-Liouville fractional derivative operator, Rearranging formula (2-1) yields (2-2) The conveyor belt stiffness and conveyor belt damping caused by the conveyor belt deflection are constant and are the conveyor belt stiffness and conveyor belt damping respectively. times, we can assume (2-3) Based on formula (2-3), a new constitutive equation is established (2-4) Performing Fourier integration on equation (2-2) yields (2-5) The complex modulus in formula (2-5) is (2-6) because ,in is the storage modulus, is the loss modulus, loss factor , it can be seen (2-7) (2-8) (2-9) According to the approximate relationship between loss factor c and damping, we can get (2-10) According to the finite element analysis method, each independent unit of the conveyor belt is regarded as a viscoelastic body, and the conveyor belt is discretized and modeled. The analysis is performed on the discrete elements, assuming that the mass of the discrete element is , the stiffness coefficient is , the damping coefficient is , the displacement is , the running resistance is According to the force condition, its dynamic equation is (2-11) in is the tensile force on the independent unit, and its magnitude is (2-12) Substituting formula (2-12) into formula (2-11) we can get (2-13).

[0005] Preferably, step S3 includes Analyze the force when the trailer does not contact the slewing wheel, and establish the balance equation of longitudinal force and resistance during the movement of the trailer (3-1) in is the friction force of the conveyor belt on the trolley device, For external resistance, is the front wheel track tangential force, is the rear wheel track tangential force; The contact point between the front wheel and the trailer track and the point of contact between the rear wheel and the trailer track Establishing the moment balance equations respectively, we can get (3-2) in is gravity, is the torque of the front wheels, is the torque of the rear wheels, is the normal support force of the front wheel, is the normal support force of the rear wheel, is the center distance between the front and rear wheels, is the horizontal distance between the center of mass of the front wheel and the center of mass of the vehicle body, is the horizontal distance between the center of mass of the rear wheel and the center of mass of the vehicle body, is the normal distance between the center of mass of the vehicle body and the contact point between the wheel and rail; According to Hamilton's principle, the vertical displacement equation of the trailer device is established as follows: (3-3) The pitch displacement equation for the vehicle body is: (3-4) in is the mass of the front wheel, is the mass of the rear wheel, is the mass of the vehicle body, is the vertical displacement of the front wheel, is the vertical displacement of the rear wheel, is the vertical displacement of the vehicle body, is the damping coefficient of the front wheel, is the damping coefficient of the rear wheel, is the damping coefficient of the vehicle body, is the stiffness coefficient of the front wheel, is the stiffness coefficient of the rear wheel, is the stiffness coefficient of the vehicle body, is the pitch angle of the vehicle body; is the moment of inertia of the vehicle body; Establishing the linear second-order differential equation of the trailer (3-5) in is the mass matrix of the trailer device; is the damping matrix of the trailer device; is the stiffness matrix of the trailer device; all of them are The square array, is the acceleration matrix of the trailer device, is the speed matrix of the trailer device, is the displacement matrix of the trailer device, is the force matrix of the towing device acting on each unit, Column vector of ; Arranging equations (3-1) to (3-4) into the matrix form of a linear second-order differential equation yields (3-6) (3-7) (3-8) (3-9) (3-10).

[0006] Preferably, step S4 includes A heavy hammer tensioning device is used, which includes a tensioning roller and a mass block. Assuming that the tensioning device is tensioned with constant force, the force balance equation of the tensioning device is established as follows: (4-1) in is the mass of the tensioning device, It is the tension on both ends of the tensioning device; definition and Respectively represent the displacement of the meeting point and separation point between the tensioning roller and the conveyor belt, is the rotation displacement of the tensioning drum, is the vertical displacement of the tensioning roller, we can get (4-2) Arrangement available (4-3) Since the conveyor belt connected to the tensioning device is a continuum, the Euler-Lagrange equation can be used to obtain the independent units of the two conveyor belts connected to the tensioning device: (4-4) (4-5) (4-6) (4-7) Establish the second-order differential equation of the tensioner (4-8) in is the tensioner mass matrix; is the tensioner damping matrix; is the tensioner stiffness matrix; all of them are The square array, is the acceleration matrix of the tensioner, is the tensioner speed matrix, is the displacement matrix of the tensioner, is the force matrix of the tensioning device acting on each unit, Column vector of ; Arranging equations (4-1) to (4-7) into the matrix form of a linear second-order differential equation yields (4-9) (4-10) (4-11) (4-12) (4-13).

[0007] Preferably, step S5 is Formulate the differential equations for the drive (5-1) in is the driving force of the driving device, is the driving roller resistance, is the driving roller diameter, is the equivalent moment of inertia, is the angular acceleration, is the conveyor belt tension, The calculation formula for the above conveyor belt tension is: (5-2) Substituting equation (5-2) into equation (5-1) yields (5-3) From the quasi-motion characteristics, we know (5-4) Substituting equation (5-4) into equation (5-3) yields (5-5).

[0008] Based on the above solution, step S6 includes The place where the conveyor belt is connected to the driving device and started first is the first unit. According to the opposite direction of the conveyor belt, the conveyor belt load section is divided into N units. The conveyor belt at the turning roller is the N+1 unit. The return section of the conveyor belt is divided into M sections, a total of N+M+1 units. The discrete model of the conveyor belt is established, and it can be obtained (6-1) in , By arranging equation (6-1) into a matrix form, we can obtain the uniform motion state of the conveyor belt under the constant force tensioning device. The differential equation of its motion is: (6-2) in is the conveyor belt mass matrix; is the conveyor belt damping matrix; is the conveyor belt stiffness matrix; all of them are The square array, is the conveyor belt acceleration matrix, is the conveyor belt speed matrix, is the conveyor belt displacement matrix, is the force matrix of the conveyor belt acting on each unit, Column vector of ; (6-3) (6-4) (6-5) (6-6) (6-7) (6-8) (6-9).

[0009] Preferably, the load-bearing section and the return section are divided into multiple independent units. Mass of each independent unit of the load-bearing section for (7-1) in For the conveyor belt line quality, is the material line quality, For the quality of the trailer line, is the unit length; Unit quality in the return section for (7-2) The mass of the drive unit is (7-3) in is the equivalent moment of inertia of the motor, is the equivalent moment of inertia of the coupling; The calculation formula of the damping coefficient at other locations except the conveyor belt is: (7-4) in is the equivalent elastic modulus, is the viscosity coefficient; The resistance of the load-bearing section is (7-5) The resistance of the return section is (7-6) in is the running resistance of the load-bearing straight section, is the running resistance of the straight line section of the return section, is the length of the conveyor, is the resistance coefficient of the conveyor belt running in the load-bearing section, , is the resistance coefficient of the conveyor belt in the return section. , The conveying inclination angle.

[0010] Preferably The initial condition is (8-1) The boundary conditions are when hour (8-2) when hour (8-3) During uniform speed operation (8-4).

[0011] Preferably, step S9 uses MATLAB software to compile the calculation process, including the following steps: S9-1. Input the trolley device dynamics model, the tensioning device dynamics model, the driving device dynamics model and the conveyor belt dynamics model; S9-2. Input dynamic parameters and set initial conditions and boundary conditions; S9-3. Determine whether the trailer device passes through the track gap. If not, proceed to step S9-6; if so, proceed to step S9-4; S9-4. Initialize the parameter matrix of the linear second-order differential equation of the trailer device and set the initial state of the trailer device; S9-5. Use MATLAB to solve the response state of the towing device and output the resistance between the towing device and the conveyor belt; S9-6. Initialize the parameter matrix of the linear second-order differential equation of the conveyor belt dynamics model and set the initial state of the conveyor belt; S9-7. Select the time step and judge the convergence of the algorithm; S9-8. Calculate the vibration state of the conveyor belt; S9-9. Calculate the vibration state using the result of the previous time step as the initial iteration value; S9-10. Determine whether the actual calculation time t is greater than the planned calculation time T. If t>T is satisfied, proceed to step S9-11. If t>T is not satisfied, return to step S9-8 to continue the calculation; S9-11. Solve the trolley device dynamics model, the tensioning device dynamics model, the driving device dynamics model and the conveyor belt dynamics model and output the dynamic response results.

[0012] Preferably, it also includes three-dimensional dynamics simulation verification, the steps of which include: S10-1. Establish a three-dimensional model of the wheel-rail belt conveyor and import it into the simulation software; S10-2. Select the Harrison start acceleration curve as the start curve of the wheel-rail belt conveyor; S10-3. Output the vibration change of the conveyor belt, the tension change of the wire rope connecting the adjacent trolleys, and the friction change between the trolleys and the conveyor belt when the conveyor belt runs at different speeds on the straight track of the load section and the return section; S10-4. Output the vibration change of the conveyor belt, the tension change of the wire rope connecting adjacent trolleys, and the friction change between the trolleys and the conveyor belt when the trolleys run at a constant speed on the straight track of the load section and the return section and the spacing between the trolleys is different; S10-5. When the output trolley device passes through the track gap at different speeds, the vibration change of the conveyor belt, the tension change of the wire rope connecting adjacent trolley devices, the friction change between the trolley device and the conveyor belt, and the track strain; S10-6. When the output trolley device passes through the track gaps of different widths at a uniform speed, the vibration changes of the conveyor belt, the tension changes of the wire ropes connecting adjacent trolley devices, the friction changes between the trolley device and the conveyor belt, and the track strain; S10-7. When the output trolley device passes through the track gaps with different height differences, the vibration changes of the conveyor belt, the tension changes of the wire rope connecting adjacent trolley devices, the friction changes between the trolley device and the conveyor belt, and the track strain.

[0013] The beneficial effects of the present invention are as follows: a dynamic model of the conveyor belt, the trolley device, the tensioning device and the driving device is established according to the actual working scenario of the wheel-rail belt conveyor, and numerical calculation simulation analysis is performed using MATLAB, which can more accurately simulate and analyze the dynamic response conditions of the vibration occurring during the movement of the conveyor belt; the MATLAB numerical simulation results are verified in combination with a three-dimensional simulation method to ensure the accuracy of the simulation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 : Schematic diagram of the installation state of the towing track and the towing device of the present invention; Figure 2 : Schematic diagram of the layered structure of the conveyor belt of the present invention; Figure 3 : Constitutive model diagram of the core layer of the conveyor belt of the present invention; Figure 4 : Model diagram of discrete units of the conveyor belt of the present invention; Figure 5 : Force analysis diagram of the towing device of the present invention; Figure 6 : Dynamic model diagram of the trailer device of the present invention; Figure 7 : Force analysis diagram of the heavy hammer type tensioning device of the present invention; Figure 8 : Dynamic model diagram of the heavy hammer type tensioning device of the present invention; Fig. 9 : Force analysis diagram of the driving device of the present invention; Fig.10 : The discrete model of the conveyor belt of the present invention; Fig.11 : MATLAB compilation flow chart of the present invention; Fig.12 : Dynamic model diagram of the towing device of the present invention when passing through the track gap; Fig.13 : Harrison acceleration curve diagram adopted by the present invention. DETAILED DESCRIPTION

[0015] The present invention will be further described below in conjunction with the accompanying drawings and embodiments: In the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be directly connected or indirectly connected through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0016] In the description of the present invention, it should be understood that the terms "center", "length", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first" and "second" are used for descriptive purposes only, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0017] In the present invention, unless otherwise clearly specified and limited, a first feature being "above" or "below" a second feature may include that the first and second features are in direct contact, or may include that the first and second features are not in direct contact but are in contact through another feature between them. Moreover, a first feature being "above", "above" and "above" a second feature includes that the first feature is directly above and obliquely above the second feature, or simply indicates that the first feature is higher in level than the second feature. A first feature being "below", "below" and "below" a second feature includes that the first feature is directly below and obliquely below the second feature, or simply indicates that the first feature is lower in level than the second feature.

[0018] A method for simulating the dynamic characteristics of a wheel-rail belt conveyor, such as Figure 1As shown, the wheel-rail belt conveyor includes a trolley track 1, a rotary wheel 2, a trolley device 3, a driving device, a conveyor belt 4 and a tensioning device. The rotary wheel and the trolley track form a closed loop structure, and the rotary wheel is arranged at both ends of the trolley track. There are multiple trolley devices, which are driven by the driving device and move on the trolley track and the rotary wheel. The trolley device includes a vehicle body and front wheels and rear wheels that are respectively connected to the front and rear ends of the vehicle body. The upper trolley track between the two rotary wheels is defined as the load-bearing section, and the lower trolley track is defined as the return section. The conveyor belt is arranged on the trolley device at the load-bearing section and the return section and moves synchronously with the trolley device. The vehicle body of the trolley device is a U-shaped structure, and the conveyor belt is arranged on the vehicle body. The conveyor belt carries the material to be transported above. When the conveyor belt and the trolley body enter the rotary wheel, the conveyor belt and the trolley body are separated, and the trolley enters the rotary wheel to change the track. After the conveyor belt is turned by the roller, it is attached to the trolley again at the return section or the load-bearing section. For the specific structure, please refer to the Chinese invention patent application “Rail belt conveyor with rotating wheel structure”, application number 201610184289.6, and the Chinese invention patent application “Rotating device and rotating method for wheel-rail belt conveyor”, application number 202310411052.7.

[0019] The downward direction perpendicular to the conveyor belt surface of the load-bearing section is defined as the vertical direction, and the moving direction of the vehicle body along the trailer track is defined as the longitudinal direction; The method for simulating the dynamic characteristics of a wheel-rail belt conveyor includes the following steps: S1. Assume that the trailer vibrates only in the vertical direction, and the force exerted by the driving device on the trailer is always in the longitudinal direction; assume that each trailer device is an independent unit, and the conveyor belt corresponding to the trailer device is defined as an independent unit, and the mass of each independent unit is concentrated at the center of mass; simplify the conveyor belt of each independent unit into a spring and a damper, where the spring is an ideal linear spring and the damper is an ideal viscous damper; S2. Since the hysteresis characteristics of the conveyor belt have a much greater impact on the conveyor belt than the relaxation characteristics during the operation of the conveyor belt, an independent unit dynamic model of the conveyor belt is established based on the Kelvin-Voigt model; Specifically, Figures 2 to 4 As shown, the conveyor belt 4 is a layered structure, including an upper cover layer 41, a belt core 42 and a lower cover layer 44 arranged in sequence, and steel wire ropes 43 are arranged at intervals in the belt core 42 layer along the width direction. A constitutive model of the belt core material and the steel wire ropes arranged at intervals along the width direction of the belt core is established, and then the balance equation of the independent unit of the conveyor belt is established. (2-1) in is the stress of the conveyor belt as a whole, is the stress on the wire rope, is the stress on the upper and lower covering layers, is the overall strain of the conveyor belt, is the strain of the wire rope, is the stress on the upper and lower covering layers, It is the volume coefficient of a single steel wire rope in the entire conveyor belt; is the elastic modulus of the wire rope, is the elastic modulus of the upper and lower covering layers, is the Riemann-Liouville fractional derivative operator, Rearranging formula (2-1) yields (2-2) The conveyor belt stiffness and conveyor belt damping caused by the conveyor belt deflection are constant and are the conveyor belt stiffness and conveyor belt damping respectively. times, we can assume (2-3) Based on formula (2-3), a new constitutive equation is established (2-4) Performing Fourier integration on equation (2-2) yields (2-5) The complex modulus in formula (2-5) is (2-6) because ,in is the storage modulus, is the loss modulus, loss factor , it can be seen (2-7) (2-8) (2-9) According to the approximate relationship between loss factor c and damping, we can get (2-10) According to the finite element analysis method, each independent unit of the conveyor belt is regarded as a viscoelastic body, and the conveyor belt is discretized and modeled. The analysis is performed on the discrete elements, assuming that the mass of the discrete element is , the stiffness coefficient is , the damping coefficient is , the displacement is , the running resistance is According to the force condition, its dynamic equation is (2-11) in is the tensile force on the independent unit, and its magnitude is (2-12) Substituting formula (2-12) into formula (2-11) we can get (2-13).

[0020] S3. Establish a mechanical equilibrium equation for the trailer device, establish the vertical displacement equation and the pitch displacement equation of the vehicle body according to the Hamilton principle, and then obtain the linear second-order differential equation of the independent unit of the trailer device; specifically, Figure 5 and Figure 6 As shown, Analyze the force when the trailer does not contact the slewing wheel, and establish the balance equation of longitudinal force and resistance during the movement of the trailer (3-1) in is the friction force of the conveyor belt on the trolley device, For external resistance, is the front wheel track tangential force, is the rear wheel track tangential force; The contact point between the front wheel and the trailer track and the point of contact between the rear wheel and the trailer track Establishing the moment balance equations respectively, we can get (3-2) in is gravity, is the torque of the front wheels, is the torque of the rear wheels, is the normal support force of the front wheel, is the normal support force of the rear wheel, is the center distance between the front and rear wheels, is the horizontal distance between the center of mass of the front wheel and the center of mass of the vehicle body, is the horizontal distance between the center of mass of the rear wheel and the center of mass of the vehicle body, is the normal distance between the center of mass of the vehicle body and the contact point between the wheel and rail; According to Hamilton's principle, the vertical displacement equation of the trailer device is established as follows: (3-3) The pitch displacement equation for the vehicle body is: (3-4) in is the mass of the front wheel, is the mass of the rear wheel, is the mass of the vehicle body, is the vertical displacement of the front wheel, is the vertical displacement of the rear wheel, is the vertical displacement of the vehicle body, is the damping coefficient of the front wheel, is the damping coefficient of the rear wheel, is the damping coefficient of the vehicle body, is the stiffness coefficient of the front wheel, is the stiffness coefficient of the rear wheel, is the stiffness coefficient of the vehicle body, is the pitch angle of the vehicle body; is the moment of inertia of the vehicle body; Establishing the linear second-order differential equation of the trailer (3-5) in is the mass matrix of the trailer device; is the damping matrix of the trailer device; is the stiffness matrix of the trailer device; all of them are The square array, is the acceleration matrix of the trailer device, is the speed matrix of the trailer device, is the displacement matrix of the trailer device, is the force matrix of the towing device acting on each unit, Column vector of ; Arranging equations (3-1) to (3-4) into the matrix form of a linear second-order differential equation yields (3-6) (3-7) (3-8) (3-9) (3-10).

[0021] S4. A mechanical equilibrium equation is established for the tensioning device, and a dynamic model of the tensioning device is established according to the Euler-Lagrange equation in combination with the independent units of the two conveyor belts adjacent to the tensioning device; specifically, Figure 7 and Figure 8 As shown, A heavy hammer tensioning device is used, which includes a tensioning roller and a mass block. Assuming that the tensioning device is tensioned with constant force, the force balance equation of the tensioning device is established as follows: (4-1) in is the mass of the tensioning device, It is the tension on both ends of the tensioning device; definition and Respectively represent the displacement of the meeting point and separation point between the tensioning roller and the conveyor belt, is the rotation displacement of the tensioning drum, is the vertical displacement of the tensioning roller, we can get (4-2) Arrangement available (4-3) Since the conveyor belt connected to the tensioning device is a continuum, the Euler-Lagrange equation can be used to obtain the independent units of the two conveyor belts connected to the tensioning device: (4-4) (4-5) (4-6) (4-7) Establish the second-order differential equation of the tensioner (4-8) in is the tensioner mass matrix; is the tensioner damping matrix; is the tensioner stiffness matrix; all of them are The square array, is the acceleration matrix of the tensioner, is the tensioner speed matrix, is the displacement matrix of the tensioner, is the force matrix of the tensioning device acting on each unit, Column vector of ; Arranging equations (4-1) to (4-7) into the matrix form of a linear second-order differential equation yields (4-9) (4-10) (4-11) (4-12) (4-13).

[0022] S5. Establish a dynamic model of the driving device; Fig. 9 As shown, Formulate the differential equations for the drive (5-1) in is the driving force of the driving device, is the driving roller resistance, is the driving roller diameter, is the equivalent moment of inertia, is the angular acceleration, is the conveyor belt tension, The calculation formula for the above conveyor belt tension is: (5-2) Substituting equation (5-2) into equation (5-1) yields (5-3) From the quasi-motion characteristics, we know (5-4) Substituting equation (5-4) into equation (5-3) yields (5-5).

[0023] S6. Combine the mathematical models of S2 and S5 to establish the overall dynamic model of the conveyor belt; Fig.10 As shown, The place where the conveyor belt is connected to the driving device and started first is the first unit. According to the opposite direction of the conveyor belt, the conveyor belt load section is divided into N units. The conveyor belt at the turning roller is the N+1 unit. The return section of the conveyor belt is divided into M sections, a total of N+M+1 units. The discrete model of the conveyor belt is established, and it can be obtained (6-1) in , By arranging equation (6-1) into a matrix form, we can obtain the uniform motion state of the conveyor belt under the constant force tensioning device. The differential equation of its motion is: (6-2) in is the conveyor belt mass matrix; is the conveyor belt damping matrix; is the conveyor belt stiffness matrix; all of them are The square array, is the conveyor belt acceleration matrix, is the conveyor belt speed matrix, is the conveyor belt displacement matrix, is the force matrix of the conveyor belt acting on each unit, Column vector of ; (6-3) (6-4) (6-5) (6-6) (6-7) (6-8) (6-9).

[0024] S7. Determine the dynamic parameters of the dynamic model in step S6, wherein the dynamic parameters include mass, stiffness, damping and external force; Divide the load section and return section into multiple independent units. Mass of each independent unit of the load-bearing section for (7-1) in For the conveyor belt line quality, is the material line quality, For the quality of the trailer line, is the unit length; Unit quality in the return section for (7-2) The mass of the drive unit is (7-3) in is the equivalent moment of inertia of the motor, is the equivalent moment of inertia of the coupling; The calculation formula of the damping coefficient at other locations except the conveyor belt is: (7-4) in is the equivalent elastic modulus, is the viscosity coefficient; The resistance of the load-bearing section is (7-5) The resistance of the return section is (7-6) in is the running resistance of the load-bearing straight section, is the running resistance of the straight line section of the return section, is the length of the conveyor, is the resistance coefficient of the conveyor belt running in the load-bearing section, , is the resistance coefficient of the conveyor belt in the return section. , The conveying inclination angle.

[0025] S8. Setting the initial conditions and boundary conditions of the dynamic model in step S6; The initial condition is (8-1) The boundary conditions are when hour (8-2) when hour (8-3) During uniform speed operation (8-4).

[0026] S9. Use numerical calculation software to compile the calculation program to simulate the vibration of the conveyor belt at the load-bearing section and the vibration of the conveyor belt passing through the track gap when the conveyor belt runs at a constant speed.

[0027] Use MATLAB software to compile the calculation process, such as Fig.11 As shown, the following steps are included: S9-1. Input the trolley device dynamics model, the tensioning device dynamics model, the driving device dynamics model and the conveyor belt dynamics model; S9-2. Input dynamic parameters and set initial conditions and boundary conditions; S9-3. Determine whether the trailer device passes through the track gap. If not, proceed to step S9-6; if so, proceed to step S9-4; S9-4. Initialize the parameter matrix of the linear second-order differential equation of the trailer device and set the initial state of the trailer device; S9-5. Use MATLAB to solve the response state of the towing device and output the resistance between the towing device and the conveyor belt; S9-6. Initialize the parameter matrix of the linear second-order differential equation of the conveyor belt dynamics model and set the initial state of the conveyor belt; S9-7. Select the time step and judge the convergence of the algorithm; S9-8. Calculate the vibration state of the conveyor belt; S9-9. Calculate the vibration state using the result of the previous time step as the initial iteration value; S9-10. Determine whether the actual calculation time t is greater than the planned calculation time T. If t>T is satisfied, proceed to step S9-11. If t>T is not satisfied, return to step S9-8 to continue the calculation; S9-11. Solve the trolley device dynamics model, the tensioning device dynamics model, the driving device dynamics model and the conveyor belt dynamics model and output the dynamic response results.

[0028] When the tractor passes through the track gap, there is a big difference between the movement of the tractor on the straight track and the movement of the tractor passing through the track gap. Therefore, it is necessary to establish a separate dynamic model for the tractor passing through the track gap. In addition, due to the collision between the wheel, rail and track, it is necessary to add a track dynamic model based on the original model, such as Fig.12 As shown, The vertical vibration equation of the vehicle passing through the track gap can be obtained from the Euler-Lagrange equation: (9-1) (9-2) (9-3) Establish the pitch displacement analysis equation for the vehicle body (9-4) in, The angle between the front and rear wheels and the track when they collide through the track gap When the track is actually built, due to technical and precision issues, the height difference between the front and rear tracks is slightly different, but the difference is not obvious, so the influence of the height difference between the front and rear tracks is ignored here. The calculation method is as follows (9-5) in is the radius of the front and rear wheels, is the track gap width.

[0029] The matrix form of the linear differential equation (9-4) is: (9-6) (9-7) (9-8) (9-9) (9-10) When the trailer passes through the track gap, the change in the height of the wheelset will generate a vertical downward speed and produce vibration, so its boundary conditions change, as shown in formula (9-11) (9-11) in is the drop height of the front and rear wheels of the trailer, , Conveyor belt speed.

[0030] It also includes three-dimensional dynamics simulation verification, the steps of which include: S10-1. Establish a three-dimensional model of the wheel-rail belt conveyor and import it into simulation software, such as ADAMS; S10-2. Select Fig.13 The Harrison starting acceleration curve shown is used as the starting curve of the wheel-rail belt conveyor; S10-3. Output the vibration change of the conveyor belt, the tension change of the wire rope connecting the adjacent trolleys, and the friction change between the trolleys and the conveyor belt when the conveyor belt runs at different speeds on the straight track of the load section and the return section; S10-4. Output the vibration change of the conveyor belt, the tension change of the wire rope connecting adjacent trolleys, and the friction change between the trolleys and the conveyor belt when the trolleys run at a constant speed on the straight track of the load section and the return section and the spacing between the trolleys is different; S10-5. When the output trolley device passes through the track gap at different speeds, the vibration change of the conveyor belt, the tension change of the wire rope connecting adjacent trolley devices, the friction change between the trolley device and the conveyor belt, and the track strain; S10-6. When the output trolley device passes through the track gaps of different widths at a uniform speed, the vibration changes of the conveyor belt, the tension changes of the wire ropes connecting adjacent trolley devices, the friction changes between the trolley device and the conveyor belt, and the track strain; S10-7. When the output trolley device passes through the track gaps with different height differences, the vibration changes of the conveyor belt, the tension changes of the wire rope connecting adjacent trolley devices, the friction changes between the trolley device and the conveyor belt, and the track strain.

[0031] The present invention is described above by way of examples, but the present invention is not limited to the above specific embodiments, and any changes or modifications made based on the present invention belong to the scope of protection claimed by the present invention.

Claims

1. A method for simulating the dynamic characteristics of a wheel-rail belt conveyor. It is characterized in that The wheel-rail belt conveyor comprises a trolley track, a rotating wheel, a trolley device, a driving device, a conveyor belt and a tensioning device. The rotating wheel and the trolley track form a closed loop structure, and the rotating wheel is arranged at both ends of the trolley track. There are multiple trolley devices, which are driven by the driving device and move on the trolley track and the rotating wheel. The trolley device comprises a vehicle body and front wheels and rear wheels which are rotatably connected at the front and rear ends of the vehicle body respectively. The upper trolley track between the two rotating wheels is defined as the load-bearing section, and the lower trolley track is defined as the return section. The conveyor belt is arranged on the trolley device at the load-bearing section and the return section and moves synchronously with the trolley device. The downward direction perpendicular to the conveyor belt surface of the load-bearing section is defined as the vertical direction, and the moving direction of the vehicle body along the trailer track is defined as the longitudinal direction; The method for simulating the dynamic characteristics of a wheel-rail belt conveyor includes the following steps: S1. Assume that the trailer vibrates only in the vertical direction, and the force exerted by the driving device on the trailer is always in the longitudinal direction; assume that each trailer device is an independent unit, and the conveyor belt corresponding to the trailer device is defined as an independent unit, and the mass of each independent unit is concentrated at the center of mass; simplify the conveyor belt of each independent unit into a spring and a damper, where the spring is an ideal linear spring and the damper is an ideal viscous damper; S2. Establish the independent unit dynamic model of the conveyor belt based on the Kelvin-Voigt model; S3. Establish a mechanical equilibrium equation for the trailer device, establish a vehicle body vertical displacement equation and a vehicle body pitch displacement equation according to the Hamilton principle, and then obtain a linear second-order differential equation of an independent unit of the trailer device; S4. Establish a mechanical equilibrium equation for the tensioning device, combine the independent units of the two conveyor belts adjacent to the tensioning device, and establish a dynamic model of the tensioning device according to the Euler-Lagrange equation; S5. Establish a dynamic model of the driving device; S6. Combine the mathematical models of S2 and S5 to establish the overall dynamic model of the conveyor belt; S7. Determine the dynamic parameters of the dynamic model in step S6, wherein the dynamic parameters include mass, stiffness, damping and external force; S8. Setting the initial conditions and boundary conditions of the dynamic model in step S6; S9. Use numerical calculation software to compile the calculation program to simulate the vibration of the conveyor belt at the load-bearing section and the vibration of the conveyor belt passing through the track gap when the conveyor belt runs at a constant speed.

2. A method for simulating dynamic characteristics of a wheel-rail belt conveyor according to claim 1, It is characterized in that Step S2 is: The constitutive model of the spacing between the core material and the steel wire rope is established along the width direction of the core, and then the equilibrium equation of the independent unit of the conveyor belt is established. （2-1） in is the stress of the conveyor belt as a whole, is the stress on the wire rope, is the stress on the upper and lower covering layers, is the overall strain of the conveyor belt, is the strain of the wire rope, is the stress on the upper and lower covering layers, It is the volume coefficient of a single steel wire rope in the entire conveyor belt; is the elastic modulus of the wire rope, is the elastic modulus of the upper and lower covering layers, is the Riemann-Liouville fractional derivative operator, Rearranging formula (2-1) yields （2-2） The conveyor belt stiffness and conveyor belt damping caused by the conveyor belt deflection are constant and are the conveyor belt stiffness and conveyor belt damping respectively. times, we can assume （2-3） Based on formula (2-3), a new constitutive equation is established （2-4） Performing Fourier integration on equation (2-2) yields （2-5） The complex modulus in formula (2-5) is （2-6） because ,in is the storage modulus, is the loss modulus, loss factor , it can be seen （2-7） （2-8） （2-9） According to the approximate relationship between loss factor c and damping, we can get （2-10） According to the finite element analysis method, each independent unit of the conveyor belt is regarded as a viscoelastic body, and the conveyor belt is discretized and modeled. The analysis is performed on the discrete elements, assuming that the mass of the discrete element is , the stiffness coefficient is , the damping coefficient is , the displacement is , the running resistance is According to the force condition, its dynamic equation is （2-11） in is the tensile force on the independent unit, and its magnitude is （2-12） Substituting formula (2-12) into formula (2-11) we can get （2-13）。 3. A method for simulating dynamic characteristics of a wheel-rail belt conveyor according to claim 1, It is characterized in that The step S3 includes Analyze the force when the trailer does not contact the slewing wheel, and establish the balance equation of longitudinal force and resistance during the movement of the trailer （3-1） in is the friction force of the conveyor belt on the trolley device, For external resistance, is the front wheel track tangential force, is the rear wheel track tangential force; The contact point between the front wheel and the trailer track and the point of contact between the rear wheel and the trailer track Establishing the moment balance equations respectively, we can get （3-2） in is gravity, is the torque of the front wheels, is the torque of the rear wheels, is the normal support force of the front wheel, is the normal support force of the rear wheel, is the center distance between the front and rear wheels, is the horizontal distance between the center of mass of the front wheel and the center of mass of the vehicle body, is the horizontal distance between the center of mass of the rear wheel and the center of mass of the vehicle body, is the normal distance between the center of mass of the vehicle body and the contact point between the wheel and rail; According to Hamilton's principle, the vertical displacement equation of the trailer device is established as follows: （3-3） The pitch displacement equation for the vehicle body is: （3-4） in is the mass of the front wheel, is the mass of the rear wheel, is the mass of the vehicle body, is the vertical displacement of the front wheel, is the vertical displacement of the rear wheel, is the vertical displacement of the vehicle body, is the damping coefficient of the front wheel, is the damping coefficient of the rear wheel, is the damping coefficient of the vehicle body, is the stiffness coefficient of the front wheel, is the stiffness coefficient of the rear wheel, is the stiffness coefficient of the vehicle body, is the pitch angle of the vehicle body; is the moment of inertia of the vehicle body; Establish the linear second-order differential equation of the trailer device （3-5） in is the mass matrix of the trailer device; is the damping matrix of the trailer device; is the stiffness matrix of the trailer device; all of them are The square array, is the acceleration matrix of the trailer device, is the speed matrix of the trailer device, is the displacement matrix of the trailer device, is the force matrix of the towing device acting on each unit, Column vector of ; Arranging equations (3-1) to (3-4) into the matrix form of a linear second-order differential equation yields （3-6） （3-7） （3-8） （3-9） （3-10）。 4. A method for simulating dynamic characteristics of a wheel-rail belt conveyor according to claim 2, It is characterized in that The step S4 includes A heavy hammer tensioning device is used, which includes a tensioning roller and a mass block. Assuming that the tensioning device is tensioned with constant force, the force balance equation of the tensioning device is established as follows: （4-1） in is the mass of the tensioning device, It is the tension on both ends of the tensioning device; definition and Respectively represent the displacement of the meeting point and separation point between the tensioning roller and the conveyor belt, is the rotation displacement of the tensioning drum, is the vertical displacement of the tensioning roller, we can get （4-2） Arrangement available （4-3） Since the conveyor belt connected to the tensioning device is a continuum, the Euler-Lagrange equation can be used to obtain the independent units of the two conveyor belts connected to the tensioning device: （4-4） （4-5） （4-6） （4-7） Establish the second-order differential equation of the tensioner （4-8） in is the tensioner mass matrix; is the tensioner damping matrix; is the tensioner stiffness matrix; all of them are The square array, is the acceleration matrix of the tensioner, is the tensioner speed matrix, is the displacement matrix of the tensioner, is the force matrix of the tensioning device acting on each unit, Column vector of ; Arranging equations (4-1) to (4-7) into the matrix form of a linear second-order differential equation yields （4-9） （4-10） （4-11） （4-12） （4-13）。 5. A method for simulating dynamic characteristics of a wheel-rail belt conveyor according to claim 2, It is characterized in that Step S5 is Formulate the differential equations for the drive （5-1） in is the driving force of the driving device, is the driving roller resistance, is the driving roller diameter, is the equivalent moment of inertia, is the angular acceleration, is the conveyor belt tension, The calculation formula for the above conveyor belt tension is: （5-2） Substituting equation (5-2) into equation (5-1) yields （5-3） From the quasi-motion characteristics, we know （5-4） Substituting equation (5-4) into equation (5-3) yields （5-5）。 6. A method for simulating dynamic characteristics of a wheel-rail belt conveyor according to claim 5, It is characterized in that Step S6 includes The place where the conveyor belt is connected to the driving device and started first is the first unit. According to the opposite direction of the conveyor belt, the conveyor belt load section is divided into N units. The conveyor belt at the turning roller is the N+1 unit. The return section of the conveyor belt is divided into M sections, a total of N+M+1 units. The discrete model of the conveyor belt is established, and it can be obtained （6-1） in , By arranging equation (6-1) into a matrix form, we can obtain the uniform motion state of the conveyor belt under the constant force tensioning device. The differential equation of its motion is: （6-2） in is the conveyor belt mass matrix; is the conveyor belt damping matrix; is the conveyor belt stiffness matrix; all of them are The square array, is the conveyor belt acceleration matrix, is the conveyor belt speed matrix, is the conveyor belt displacement matrix, is the force matrix of the conveyor belt acting on each unit, Column vector of ; （6-3） （6-4） （6-5） （6-6） （6-7） （6-8） （6-9）。 7. A method for simulating dynamic characteristics of a wheel-rail belt conveyor according to claim 1, It is characterized in that Divide the load section and return section into multiple independent units. Mass of each independent unit of the load-bearing section for （7-1） in For the conveyor belt line quality, is the material line quality, For the quality of the trailer line, is the unit length; Unit quality in the return section for （7-2） The mass of the drive unit is （7-3） in is the equivalent moment of inertia of the motor, is the equivalent moment of inertia of the coupling; The calculation formula of the damping coefficient at other locations except the conveyor belt is: （7-4） in is the equivalent elastic modulus, is the viscosity coefficient; The resistance of the load-bearing section is （7-5） The resistance of the return section is （7-6） in is the running resistance of the load-bearing straight section, is the running resistance of the straight line section of the return section, is the length of the conveyor, is the resistance coefficient of the conveyor belt running in the load-bearing section, , is the resistance coefficient of the conveyor belt in the return section. , The conveying inclination angle.

8. A method for simulating dynamic characteristics of a wheel-rail belt conveyor according to claim 6, It is characterized in that The initial condition is （8-1） The boundary conditions are when hour （8-2） when hour （8-3） During uniform speed operation （8-4）。 9. A method for simulating dynamic characteristics of a wheel-rail belt conveyor according to claim 1, It is characterized in that Step S9 uses MATLAB software to compile the calculation process, including the following steps: S9-1. Input the trolley device dynamics model, the tensioning device dynamics model, the driving device dynamics model and the conveyor belt dynamics model; S9-2. Input dynamic parameters and set initial conditions and boundary conditions; S9-3 determines whether the trailer device passes through the track gap. If not, proceed to step S9-6; if so, proceed to step S9-4; S9-4. Initialize the parameter matrix of the linear second-order differential equation of the trailer device and set the initial state of the trailer device; S9-5. Use MATLAB to solve the response state of the towing device and output the resistance between the towing device and the conveyor belt; S9-6. Initialize the parameter matrix of the linear second-order differential equation of the conveyor belt dynamics model and set the initial state of the conveyor belt; S9-7. Select the time step and judge the convergence of the algorithm; S9-8. Calculate the vibration state of the conveyor belt; S9-9. Calculate the vibration state using the result of the previous time step as the initial iteration value; S9-10. Determine whether the actual calculation time t is greater than the planned calculation time T. If t>T is satisfied, proceed to step S9-11. If t>T is not satisfied, return to step S9-8 to continue the calculation; S9-11. Solve the trolley device dynamics model, the tensioning device dynamics model, the driving device dynamics model and the conveyor belt dynamics model and output the dynamic response results.

10. A method for simulating dynamic characteristics of a wheel-rail belt conveyor according to claim 1, It is characterized in that It also includes three-dimensional dynamics simulation verification, the steps of which include: S10-1. Establish a three-dimensional model of the wheel-rail belt conveyor and import it into the simulation software; S10-2. Select the Harrison start acceleration curve as the start curve of the wheel-rail belt conveyor; S10-3. Output the vibration change of the conveyor belt, the tension change of the wire rope connecting the adjacent trolleys, and the friction change between the trolleys and the conveyor belt when the conveyor belt runs at different speeds on the straight track of the load section and the return section; S10-4. Output the vibration change of the conveyor belt, the tension change of the wire rope connecting adjacent trolleys, and the friction change between the trolleys and the conveyor belt when the trolleys run at a constant speed on the straight track of the load section and the return section and the spacing between the trolleys is different; S10-5. When the output trolley device passes through the track gap at different speeds, the vibration change of the conveyor belt, the tension change of the wire rope connecting adjacent trolley devices, the friction change between the trolley device and the conveyor belt, and the track strain; S10-6. When the output trolley device passes through the track gaps of different widths at a uniform speed, the vibration changes of the conveyor belt, the tension changes of the wire ropes connecting adjacent trolley devices, the friction changes between the trolley device and the conveyor belt, and the track strain; S10-7. When the output trolley device passes through the track gaps with different height differences, the vibration changes of the conveyor belt, the tension changes of the wire rope connecting adjacent trolley devices, the friction changes between the trolley device and the conveyor belt, and the track strain.

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